解：（1）单调递减设在(0,+∞）有x1,x2(x1＜x2)f(x1)-f(x2)=(x1+x2)(x1-x2)+1/x1^2-1/x2^2=(x1^2-x2^2)(x1x2-1)/x1x2∵x₁²-x₂²＜0,x1x2-1＜0∴f(x1)-f(x2)＞0,f(x1)＞f(x2)∴单调递减（2）在（-∞,0)增，(0,+∞）减
